The Event Structure is really just an abstraction that hides the thread of execution from you. There has to be some code running somewhere on the computer that is checking for these events and then calling your event handlers. in C, you'd be expected to provide this code (the "main loop" of the program) yourself. This code would check the various event sources you are interested in and call your event handler functions.
The trick then becomes how to not have this main loop wildly spinning the CPU. One easy trick is to have the main loop sleep for a period of time and then check if any events need to be handled, and then sleep again. This has the downside of introducing latency. A better trick, when applicable, is to have the Operating System do these checks as part of its normal operations, and then wake your application's main loop up when something interesting happened. In Linux, this is done with the 'select' system call, but select has the limitation that it can only specify a resource that can be associated with a file descriptor, so devices, stdin, files, network ports are fine.
Edit: To clarify for my downvoters: I am not denying the existance of hardware interrupts. Yes, in cases where code has direct access to hardware interrupts for all events that it wishes to handle (such as an embedded system or device driver) you can write truly "event driven" code with multiple entry points that does not busy wait or sleep. However, in a normal application level C program running under Linux, this code architecture does not literally exist but is emulated at the application level. Any Linux application is going to have a main loop, and at least one thread of execution. This thread may get paused by the scheduler, but it always exists and always has an instruction pointer at a particular instruction. If the code leaves the main() the program ends. There is no facility for the code to return from main and get a callback later on from the kernel. The code has a single entry point and must call its various event handlers manually. Other than in a device driver (or very specific system code using signals), you can not have the kernel or hardware automatically call a certain function if the user clicked on a certain menu item, instead your code is running, detects this event itself, and calls the correct event handler.
You can tell LabView "Call this function when XX happens". In C, you tell your own event dispatch code "Call this function when XX happens".
What I'm trying to say (poorly?) is that the Event framework architecture is not native to a C / Linux application. It must be emulated by your code by having a main dispatch thread that gives the appearance of an event driven framework. Either you do this manually, or use an event library that does this behind the scenes to give the appearance of an event driven model. LabView takes the second approach, so it appears that no code is running when no events are happening, but in reality there is LabView's own C++ code running managing the event queues. This doesn't mean that it is busy waiting all the time, as I said before there are system calls such as select and sleep that the code can use to yield cpu time when it has no work to do, but the code can not simply stop executing.
Lets say you want to write an "event driven" program with two event handlers. One that gets called every ten seconds called tick() and one that gets called every time a key gets pressed called key(), and one that gets called everytime the word "foobar" gets typed called foobar(). You can define these three event handlers, but in addition you need some dispatch main thread that basically does
while not quitting
If 10 seconds have elapsed, call tick()
If Key has been Pressed
call key()
add save the key to our key buffer
If buffer now contains "foobar" call foobar() and clear buffer
Wait()
If all of the events you care about are system level events or time level events, you can Wait() can simply be telling the kernel 'wake me up when one of these things happens' so I don't need to 'busy wait', But you can't simply tell the Kernel "call foobar() when "foobar is pressed". You have to have application level dispatch code that emulates the Event Structure. You're C program only has a single entry point from the kernel for each thread of execution. If you look at libraries that provide event dispatch models, such as Qt, you will find that they are working like this under the hood.